We compute the similarity matrix between 3-letter profiles using the expression given by eq:sim with a coefficient of one third for each term (none of the similarities is preferred to the two others) and the dot product as inner product. For clustering, we use the
k-means algorithm and choose the number of clusters with the silhouette method [1]}. This method calculates an average silhouette score \(\overline{s}(k) \in [-1;1]\)  that estimates the quality of a partition into \(k\)  clusters through the difference between the mean intra-cluster distance \(a(u)\)  of a point \(u\)  (the average distance from \(u\)  to the points of the cluster it has been assigned to) and the mean nearest-cluster distance \(b(u)\)  (the average distance to the nearest cluster to which the point \(u\)  does not belong).
For each data set and \(k\)  clusters, the average silhouette score is:
\( \overline{s}(k)=\frac{1}{|V|} \sum _{u \in V}\;\frac{b(u)-a(u)}{\max \lbrace a(u),b(u)\rbrace } \) 
